Question

1. a gas fills a 1.50 l container with a pressure of 110 kpa at 47 °c. of the following calculations, which one would be used to calculate the new volume of the gas at satp?

(320k)(100kpa)(1.50l)
(298k)(110kpa)
(298k)(110kpa)(1.50l)
(320k)(100kpa)
(320k)(110kpa)(1.50l)
(298k)(100kpa)
(298k)(100kpa)(1.50l)
(320k)(110kpa)

Explanation:

Step1: Convert temperatures to Kelvin

$T_1 = 47^{\circ}C+273 = 320K$, $T_2$ at SATP is $25^{\circ}C + 273=298K$. SATP pressure $P_2 = 100kPa$, initial pressure $P_1 = 110kPa$, initial volume $V_1=1.50L$.

Step2: Use the combined - gas law formula

The combined - gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$, and we can solve for $V_2$. Rearranging gives $V_2=\frac{P_1V_1T_2}{P_2T_1}$.

Step3: Substitute values

Substitute $P_1 = 110kPa$, $V_1 = 1.50L$, $T_1 = 320K$, $P_2 = 100kPa$, $T_2 = 298K$ into the formula for $V_2$. So $V_2=\frac{(320K)(110kPa)(1.50L)}{(298K)(100kPa)}$.

Answer:

$\frac{(320K)(110kPa)(1.50L)}{(298K)(100kPa)}$ (first option)